How many liters of a 25% saline solution
must be mixed with 4 liters of a 40% saline
solution to make a 30% saline solution?

The expressions given in the questions mean that the least common denominator is the least common multiple.

According to the question,

We have the following information:

We have three questions of fractions which are either in addition or subtraction.

Now, we will only look at the denominators of these fractions. And note that the least common multiple is same as the least common denominator.

For first one, it is 6 and 4:

Each multiple of 6: 2*3

Multiples of 4:2*2

The least common multiple of 6 and 4: 12

The least common denominator is 12.

For second one, it is 7 and 3.

Each multiple of 7: 7

Multiple of 3: 3

The least common multiple of 7 and 3: 21

The least common denominator of 7 and 3: 21

For third one, it is 8 and 2.

Multiples of 8: 2*2*2

Multiples of 2: 2

The least common multiple of 8 and 2: 8

The least common denominator is 8.

Hence, the expressions given in the questions mean that it is the least common multiple.

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Simplification of the given expression ( a + b ) / ( a - b ) for the given values of a and b is equal to ( 4 / 1 ).

As given in the question,

Given expression:

( a + b ) / ( a - b )

Simplification of the given expression ( a + b ) / ( a - b ) for the value

a = 5 and b = 3 is given by,

( a + b ) / ( a - b ) we get,

( a + b ) / ( a - b )

= ( 5 + 3 ) / ( 5 - 3)

= ( 8 ) / ( 2 )

= ( 4 × 2 ) / ( 2 )

= ( 4 / 1 )

Therefore, simplification of the given expression ( a + b ) / ( a - b ) for the given values of a and b is equal to ( 4 / 1 ).

The complete question is:

Simplify the given expression:

(a + b)/ (a -b) = ?

For a=5 and b=3

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[tex]{ \purple{ \tt{x = 3}}}[/tex]

[tex]{ \blue{ \sf{ {6}^{2} - x - 12 = 0}}}[/tex]

[tex]{ \blue{ \sf{36 - x - 12 = 0}}}[/tex]

Take 12 as common

[tex]{ \blue{ \sf{ \cancel{12}(3 - x) { \cancel{-12} = 0}}}}[/tex]

[tex]{ \blue{ \sf{3 - x = 0}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \tt \overbrace{ \underbrace{x = 3}}}}}}[/tex]

Answer:

see explanation

Step-by-step explanation:

the median is a segment that goes from the vertex of a triangle to the midpoint of the opposite side.

Then Q is the midpoint of PR

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

use this formula to find the coordinates of Q

with (x₁, y₁ ) = R (0, 2b ) and (x₂, y₂ ) = P (2a, 0 )

Q = ( [tex]\frac{0+2a}{2}[/tex] , [tex]\frac{2b+0}{2}[/tex] ) = ( [tex]\frac{2a}{2}[/tex] , [tex]\frac{2b}{2}[/tex] ) = (a, b )

---------------------------------------------------

use the distance formula to find the lengths of median MQ and hypotenuse PR of Δ MRP

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = M (0, 0 ) and (x₂, y₂ ) = Q (a, b )

MQ = [tex]\sqrt{(a-0)^2+(b-0)^2}[/tex] = [tex]\sqrt{a^2+b^2}[/tex]

repeat with (x₁, y₁ ) = P (2a, 0 ) and (x₂, y₂ ) = R (0, 2b )

PR = [tex]\sqrt{(0-2a)^2+(2b-0)^2}[/tex]

     = [tex]\sqrt{(-2a)^2+(2b)^2}[/tex]

     = [tex]\sqrt{4a^2+4b^2}[/tex]

     = [tex]\sqrt{4(a^2+b^2)}[/tex]

     = 2[tex]\sqrt{a^2+b^2}[/tex]

then MQ is half PR

Answer:

I got (-1,-4) and (3,0) When I graphed with Desmos.  I do no see that solution.

Step-by-step explanation:

The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.

The expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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Answer:

Step-by-step explanation: 9091.6

Answer:

9091.6

Step-by-step explanation:

Answer:

45.90

Step-by-step explanation:

$60.00 15% off = $51.00

$51.00 10% off = 45.90

Answer:

5

Step-by-step explanation:

5 + 2 = 7

7(3) = 21

_

5 + 16 = 21

The number of different codes as the letters A or C must come first and digits can be repeated is 2000

Permutations and combinations are a subset of the study of finite, discrete structures that are known as combinatorics. Combinations include the selection of items without respect to order, whereas permutations are precise selections of elements within a set where the order of the elements is significant.  

Here we have,

The locker combination code consists of one letter and 3 digits  

Here we need to find the number of different codes If the letter A or C must come first and digits can be repeated.

Given that the first letters are A and C

Here number of ways that A and C can be chosen at first = 2

As we know Number of digits = 10  [ including 0, 0 to 9 ]

Number of arrangements that can be chosen from 10 digits

= 10 × 10 ×10   [ Since repetition is allowed ]  

Therefore,

The possible number of different codes = 2 × 10 × 10 ×10 = 2000

Therefore

The number of different codes as the letters A or C must come first and digits can be repeated is 2000

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Answer:

m = -5/3

Step-by-step explanation:

Slope is defined as the change in y / change in x or [tex]\frac{y2-y1}{x2-x1}[/tex]

The order of the points don't matter so we can do:

[tex]\frac{-1-(-6)}{5-8}=\frac{-5}{3}[/tex]

-5/3 is as simple as the fraction can be.

Answer:

  3 g

Step-by-step explanation:

You want to know the mass of thyme that must be added to 12 g of a spice mix that is 25% thyme in order to make it 40% thyme.

Let t represent the amount of added thyme (in grams). The amount of thyme in the augmented mix is ...

  0.25(12) + t = 0.40(12 +t)

Simplifying the equation gives ...

  3 +t = 4.8 +0.40t

  0.6t = 1.8 . . . . . . . . . subtract 0.40t +3

  t = 3 . . . . . . . . . . . divide by 0.6

3 grams of thyme must be added to the mix.

1. The equation in​ a slope-intercept form describing the relationship is y = -4000x + 27000.

2. The daily sales of Fun Noodles at the price of $5.50 is  5000.

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $5, sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 3000 Fun Noodles per day.

The relationship between sales​ price, x, and the number of Fun Noodles​ sold, ​ y, is linear. The ordered pair are (5, 7000) and (6, 3000).

The equation in slope intercept form describing the relationship is as follows:

1. y = mx + b

where

Therefore,

m = 3000 - 7000 / 6 - 5

m = - 4000

Let's find the y-intercept using (6, 3000)

3000 = -4000(6) + b

3000 + 24000 = b

27000 = b

Hence, the equation is y = -4000x + 27000

2. The daily sales of Fun Noodles at the price of $5.50 can be computed as follows;

y = -4000(5.5) + 27000

y = -22000 + 27000

y = 5000

Therefore, the daily sales is 5000.

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Answer:2

Step-by-step explanation: I don’t have a explanation

Answer: 2

Step-by-step explanation:

You should be able to do this...

The equation of a line is y=-1/4x-7, (option 1)

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

Write the equation in the form y = mx + b to find the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept.

Given:-

Equation of the line is y=4x+8 

The point through which the line passes (-8,4).

here the slope of the line is m1=4

To find the perpendicular line we know the formula

m1*m2=-1

By putting the value of m1 we get m2= -1/4

By using the one-point formula of the line we have

=>(y-y1)=m2*(x-x1)

By putting the values of y1 and x1 we get

(y1,x1)=(-8,4)

=>(y+8)=-0.25*(x-4)

y+0.25x+7=0

Hence the desired equation of the line is y=-1/4x-7

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Answer:

The numerator is the top number of a fraction.

your welcome! <3

Answer:

Numerator is on the the top of the fraction

Step-by-step explanation:

x

_     x is the numerator

y

1) The percentage of students who will get a score below 275 is; 0.15%

2) Yes, any score below 275 is significantly different from the mean.

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

1) We are given;

Population mean; μ = 500

Sample mean; x' = 275

standard deviation; σ = 75

Thus;

z = (275 - 500)/75

z = -3

This is 3 standard deviations from the mean. Thus;

The percentage of students who will get a score below 275 is;

(100 - 99.7)/2 = 0.15%

2) Yes, any score below 275 is more than 3 standard deviations away from the mean and can be considered significantly different from the mean.

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The order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

The given decimal number are 4.5, 3.9, 4.25, 3.75, 4.2

Numerical order is a way of arranging a sequence of numbers. This could be in ascending or descending order.

Ascending order: Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

The order of decimal numbers

Now, least to greatest of decimal numbers is

3.75<3.9<4.2<4.25<4.5

Therefore, the order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

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Answer: The answer is 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

l = length

w = width = 2.5

a = area = 12.5

l = a/w = 12.5/2.5 = 5

so the answer is l = 5

Answer: PEMDAS

Parenthesis exponents multiplication Division addition subtraction

Step-by-step explanation:

solve (x+1) first then after just follow pemdas  

Answer:

Below

Step-by-step explanation:

If she buys a loaf of bread she has   only 6 dollars for tomatoes

   $ 6 / 1.20 $/POUND = 5 POUNDS OF TOMATOES

(8-2) / 1.20 = # TOMATOES

A property which is used in the calculation above is: Commutative Property of Multiplication.

The Commutative Property of Multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged and grouped.

This ultimately implies that, re-arranging or regrouping the order of numbers that are being multiplied does not change the end result (output) or product.

Mathematically, the Commutative Property of Multiplication is represented by this mathematical expression:

a · (b) = b · (a)

By applying the Commutative Property of Multiplication to the calculation, we have:

(64⋅25)⋅4 = 6400

64⋅(25⋅4) = 6400

64⋅(100) = 6400

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Answer:

0

Step-by-step explanation:

if we x and y = 0

if we have 3x + 3y= 0

The compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

A construction worker earns an average bi-weekly net pay of $1,764.00.

= 10% of 1764

= (10/100)1764

= $176.4

= 20% of 1764

= (20/100)1764

= $352.8

Inequality will be: $176.40 ≤ t ≤ $352.80

Thus, the compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.

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Answer:

$382.20 ≤ t ≤ $764.40

Step-by-step explanation:

Hello, so first we would need to convert bi-weekly pay to monthly income.

First we would times $1,764.00 by 26

1764.00 × 26 = 45864

Then we would divide 45864 by 12

45864 ÷ 12 = 3822.

Then we calculate how much the worker can spend  if their monthly budget for food is in between 10% and 20%

3822 ×  10% = 382.20

3822 × 20% = 764.40

So, we can see the correct answer is $382.20 ≤ t ≤ $764.40.

Answer:
30-2=28+542=570

Step-by-step explanation:

The population variance of the given data is 3.2.

Given  Σ(x - 38)² = 64 .

We know that the population variance of the data is the square of the standard deviation.

Now the standard deviation for the population is given by

σ =√(Σ(x - 38)² / N)

Again variance = σ ²

Let us first calculate σ .

σ = √(64/20) = √3.2

variance

= σ ²

= (√3.2)²

= 3.2

Therefore the variance of the population is 3.2

In probability theory and statistics, variance is the predicted squared variation of a random variable from its population mean or sample mean. Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance.

A few ideas that use variance include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.

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In the given ΔDEF x is 17 units and y is 2 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, GH is the midpoint of ΔDEF and EF is the base of the ΔDEF with a length of 28 units.

We know the midpoint of ΔDEF is (1/2) EF.

∴ GH = (28/2) = 14 units.

Now GH = x - 3.

14 = x - 3.

x = 17.

Given DH and FH are equal.

∴ y + 8 = x - 7.

y + 8 = 17 - 7.

y + 8 = 10.

y = 2.

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Answer:

a = 30

Step-by-step explanation:

I am not exactly sure what the question is asking but if referring to right triangles, the Pythagorean theorem would work best.

Formula :

[tex]a^2 + b^2 = c^2\\\\[/tex]

Substitute values :

[tex]a^2 + 40^2 = 50^2\\a^2 + 1600 = 2500[/tex]

Solve for a:

[tex]a = \sqrt{2500 - 1600} \\a = 30[/tex]

** you could also use the 3:4:5 ratio

Answer:

1/2

Step-by-step explanation:

u replace x with -3

=4(2)-³

=4(0.125)

=0.5

=1/2